The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in context its Bethe ansatz solution. It is found that anyonic statistical parameter and dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons fermions. Moreover, may trigger beyond Fermi for which alpha greater than one. Tonks-Girardeau weak limits detail. results support universal role dispersion relations.

We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas an external field. The diagram, critical fields, magnetization, local correlation are obtained analytically via exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when field $H<{H}_{c1}$. A completely ferromagnetic without occurs $H>{H}_{c2}$. In region ${H}_{c1}<H<{H}_{c2}$, we observe mixed...

A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of standard pairing problem is established based on Heine-Stieltjes correspondence. For $k$ pairs valence nucleons $n$ different single-particle levels, it found that solutions can be obtained from one (k+1)x(k+1) and (n-1)x(k+1) matrices, which are associated with extended Van Vleck polynomials, respectively. Since coefficients in these polynomials free divergence variations contrast to original equations, thus...

Abstract The evolution of nuclear shape and rotational behavior along the yrast line in even-even 126-136 Ba has been systematically investigated using pairing self-consistent Woods-Saxon-Strutinsky calculation combined with total Routhian surface (TRS) method (β 2 , γ, β 4 ) deformation space. Empirical laws are applied to evaluate ground-state properties, revealing a from axially deformed non-axial vibrational configuration isotopes. Particularly, an extreme γ-unstable is predicted 130 Ba....

We show that below the degenerate temperature distribution profiles of strongly interacting anyons in one-dimension coincide with most probable distributions ideal particles obeying generalized exclusion statistics (GES). In regime thermodynamics and local two-particle correlation function derived from GES are seen to agree for low temperatures results anyon model using thermodynamic Bethe ansatz. The anyonic dynamical interactions implement a continuous range GES, providing signature...

The exact solution of the one-dimensional interacting mixed boson-fermion gas is used to calculate ground-state properties both for finite systems and in thermodynamic limit. quasimomentum distribution, energy, generalized velocities are obtained as functions interaction strength polarized nonpolarized fermions. We do not observe any demixing instability system repulsive interactions.

Chiral BIC can reach ultrahigh quality factors (Q-factor) based on its asymmetry, with broken mirror symmetries and in-plane inversion. Only by structural perturbation chiral quasi-BIC (q-BIC) appear, so it is much more realizable reasonable for the manufacturers in practical productions fabrications considering technology means that are available. In this paper, we design a new dielectric metasurface employing H-shaped silica meta-atoms lattice, which symmetrical structure, obtaining...

(abbreviated) This article considers recent advances in the investigation of thermal and magnetic properties integrable spin ladder models their applicability to physics real compounds. The ground state two-leg spin-1/2 mixed spin-(1/2,1) at zero temperature are analyzed by means Thermodynamic Bethe Ansatz. Solving TBA equations yields exact results for critical fields behaviour. investigated terms recently introduced High Temperature Expansion method, which is discussed detail. It shown...

We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions external fields. Exact results for ground-state energy, critical fields, magnetization diagrams are obtained analytically from Bethe ansatz solutions. Driven by Zeeman splitting, system shows exotic phases bound pairs, a normal Fermi liquid, four mixtures these states. Particularly, smooth transition trionic into pairing occurs as highest...

We calculate the Wilson ratio of one-dimensional Fermi gas with spin imbalance. The attractively interacting fermions is solely determined by density stiffness and sound velocity pairs excess for two-component Tomonaga-Luttinger liquid phase. exhibits anomalous enhancement at two critical points due to sudden change in states. Despite a breakdown quasiparticle description one dimension, important features are retained; namely, specific heat linearly proportional temperature, whereas...

We consider the integrable one-dimensional δ-function interacting Bose gas in a hard wall box which is exactly solved via coordinate Bethe ansatz. The ground-state energy, including surface derived from Lieb–Liniger-type integral equations. leading and correction terms are obtained weak strong coupling regimes both discrete equations This allows investigation of finite-size boundary effects model. also study Luttinger liquid behaviour by calculating parameters correlations. conditions seen...

We provide evidence in support of a recent proposal by Astrakharchik at al. for the existence super Tonks-Girardeau gas-like state attractive interaction regime quasi-one-dimensional Bose gases. show that Tonks-Giradeau corresponds to highly-excited Bethe integrable interacting gas which bosons acquire hard-core behaviour. The properties vary smoothly throughout wide range from strong repulsion attraction. There is an additional stable phase this form two-body bound states behaving like bosons.

We investigate magnetic properties and statistical effects in one-dimensional (1D) strongly repulsive two-component fermions a 1D mixture of polarized bosons. Universality the characteristics phase transitions, magnetization, susceptibility presence an external field $H$ are analyzed from exact thermodynamic Bethe ansatz solution. show explicitly that with interaction have antiferromagnetic behavior at zero temperature. A universality class linear field-dependent magnetization persists for...

A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears universal relations among thermodynamic quantities, such as large momentum tails, energy, and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open to whether or not contact can signify phase transitions that are insensitive short-range physics. Here we show that, near continuous classical...

Ground-state phase transitions in odd nuclei are examined. Especially, the odd-odd revealed. It is found that odd-even effects may reach their maximal or minimal values around critical point at $N=90$; signals of transition greatly enhanced relative to those adjacent even-even species. Moreover, a pairing model analysis Sm isotopes indicates behaviors related be driven by decrease pair strength $G$ with sudden flattening $\ensuremath{\Delta}G$ point.

A new step-by-step diagonalization procedure for evaluating exact solutions of the nuclear deformed mean-field plus pairing interaction model is proposed via a simple Bethe ansatz in each step from which eigenvalues and corresponding eigenstates can be obtained progressively. This approach draws upon an observation that original one- two-body problem $k$-particle Hilbert subspace mapped onto one-body grand hard-core boson picture solved by with known earlier work. Based on this procedure, it...

A simple set of algebraic equations is derived for the exact low-temperature thermodynamics one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear splitting, physics gapless phase at low temperatures belongs to universality class a two-component asymmetric TLL corresponding spin-neutral N-atom composites spin-(N-1)/2 single atoms. The equation...

We investigate the low temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via thermodynamic Bethe ansatz method. The exact model a weak is derived help Wiener-Hopf techniques. It turns out that energy physics can be described by spin-charge separated conformal theories effective Tomonaga-Luttinger liquid antiferromagnetic SU(2) Heisenberg spin chain. However, these two types conformally invariant...

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling at criticality using polylog function in framework of Yang-Yang thermodynamic equations. show that correlation has value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ critical regime, TLL phase quasi-classical region, where $p$...

The effect of pairing correlations on the spectral statistical behavior spherical mean-field plus standard model is investigated based exact solutions obtained from extended Heine-Stieltjes correspondence. It found that varying interaction strength $G$ in alters properties spectrum model. regular when nonzero and either well below or beyond critical region normal (localized) to superconducting (pair condensate) phase transition model, through which it likely display features chaotic...

Abstract All-dielectric metasurface with ultra-high quality resonances underpinned by bound states in the continuum (BICs) have attracted lots of attention recent years for they enable new methods wavefront control and light focusing. We study a composed one transverse nanohole (TNs) two identical vertical nanoholes (VNs) lattice, which supports both symmetry-protected accidental BICs (at-Γ off-Γ BICs). Based on destructive interference between surface from TN element VNs element, at-Γ...

We discuss recent results on the relation between strongly interacting one-dimensional Bose gas and a of ideal particles obeying nonmutual generalized exclusion statistics (GES). The thermodynamic properties considered include statistical profiles, specific heat local pair correlations. In strong coupling limit γ → ∞, Tonks-Girardeau gas, equivalence is with Fermi statistics. deviation from during boson fermionization for finite but large interaction strength described by α ≈ 1 - 2/γ, where...

Using exact Bethe ansatz solutions, we show that a spin-down fermion immersed into fully polarized spin-up Fermi sea with weak attraction is dressed by the surrounding fermions to form one-dimensional analog of polaron. As becomes strong, binds one tightly bound molecule. Throughout whole interaction regime, crossover from polaron molecule state demonstrated through results excitation spectrum, effective mass, binding energy and kinetic energy. Furthermore, clear distinction between...